Cost minimization in the predesign of an enzymatic CSTR: an overall approach

The balance equations pertaining to the modelling of a CSTR performing an enzyme-catalyzed reaction in the presence of enzyme deactivation are developed. Combination of heuristic correlations for the size-dependent cost of equipment and the purification-dependent cost of recovery of product with the mass balances was used as a basis for the development of expressions relating a (suitably defined) dimensionless economic parameter with the optimal outlet substrate concentration under the assumption that overall production costs per unit mass of product were to be minimized. The situation of Michaelis-Menten kinetics for the substrate depletion and first order kinetics for the deactivation of enzyme (considering that the free enzyme and the enzyme in the enzyme/substrate complex deactivate at different rates) was explored, and plots for several values of the parameters germane to the analysis are included.List of Symbols C _E mol m^–3 concentration of active enzyme - C _E,0 mol m^–3 initial concentration of active enzyme - C _p mol m^–3 concentration of product of interest - C _s mol m^–3 concentration of substrate - C _s,0 mol m^–3 initial concentration of substrate - I $ capital cost of equipment - k _d s^–1 deactivation constant of free enzyme - k _d s^–1 deactivation constant of enzyme in enzyme/substrate complex - K _m mol m^–3 Michaelis-Menten constant - K _m dimensionless counterpart of K _m - k _r s^–1 rate constant associated with conversion of enzyme/substrate complex into product - M _w kg mol^–1 molecular weight of product of interest - P $ kg^–1 cost of recovery of product of interest in pure form - Q m³s^–1 volumetric flow rate - V m³ volume of reactor - X $ kg^–1 global manufacture cost of product of interest in pure form - X dimensionless counterpart of X Greek Symbols ₁ $ m^–1.8 constant - ₂ $ m^–3 constant - t s useful life of CSTR - ₀ ratio of initial concentrations of enzyme and substrate - ratio of deactivation constant of free enzyme to rate constant of depletion of substrate - ratio of deactivation constants - univariate function expressing the dependence of the rate of enzyme deactivation on C _S - univariate function expressing the dependence of the rate of substrate depletion on C _S - dimensionless economic parameter     

Cell recycling studies for α-amylase production by Bacillus amyloliquefaciens

Production of -amylase by a strain of Bacillus amyloliquefaciens was investigated in a cell recycle bioreactor incorporating a membrane filtration module for cell separation. Experimental fermentation studies with the B. amyloliquefaciens strain WA-4 clearly showed that incorporating cell recycling increased -amylase yield and volumetric productivity as compared to conventional continuous fermentation. The effect of operating conditions on -amylase production was difficult to demonstrate experimentally due to the problems of keeping the permeate and bleed rates constant over an extended period of time. Computer simulations were therefore undertaken to support the experimental data, as well as to elucidate the dynamics of -amylase production in the cell recycle bioreactor as compared to conventional chemostat and batch fermentations. Taken together, the simulations and experiments clearly showed that low bleed rate (high recycling ratio) various a high level of -amylase activity. The simulated fermentations revealed that this was especially pronounced at high recycling ratios. Volumetric productivity was maximum at a dilution rate of around 0.4 h^–1 and a high recycling ratio. The latter had to exceed 0.75 before volumetric productivity was significantly greater than with conventional chemostat fermentation.List of Symbols a proportionality constant relating the specific growth rate to the logarithm of G (h) - a ₁ reaction order with respect to starch concentration - a ₂ reaction order with respect to glucose concentration - B bleed rate (h^–1) - C starch concentration (g/l) - C ₀ starch concentration in the feed (g/l) - D dilution rate (h^–1) - D _E volumetric productivity (KNU/(mlh)) - e intracellular -amylase concentration (g/g cell mass) - E extracellular -amylase concentration (KNU/ml) - F volumetric flow rate (l/h) - G average number of genome equivalents of DNA per cell - k _l intracellular equilibrium constant - k ₂ intracellular equilibrium constant - k _s Monod saturation constant (g/l) - k ₃ excretion rate constant (h^–1) - k _d first order decay constant (h^–1) - k _gl rate constant for glucose production - k _st rate constant for starch hydrolysis - k _t1 proportionality constant for -amylase production (gmRNA/g substrate) - k ₁ translation constant (g/(g mRNAh)) - KNU kilo Novo unit - m maintenance coefficient (g substrate/(g cell massh)) - n number of binding sites for the co-repressor on the cytoplasmic repressor - Q repression function K₁/K₂Q1.0 - R ratio of recycling - R _s rate of glucose production (g/lh) - r _c rate of starch hydrolysis (g/(lh)) - R _eX retention by the filter of the compounds X: starch or -amylase - r intracellular -amylase mRNA concentration (g/g cell mass) - r _C volumetric productivity of starch (g/lh) - r _E volumetric productivity of intracellular -amylase (KNU/(g cell massh)) - r _r volumetric productivity of intracellular mRNA (g/(g cell massh)) - r _e volumetric productivity of extracellular -amylase (KNU/(mlh)) - r _s volumetric productivity of glucose (g/(lh)) - r _X volumetric productivity of cell mass (g/(lh)) - S ₀ free reducing sugar concentration in the feed (g/l) - S extracellular concentration of reducing sugar (g/1) - t time (h) - V volume (l) - X cell mass concentration (g/l) - Y yield coefficient (g cell mass/g substrate) - Y _E/S yield coefficient (KNU -amylase/g substrate) - Y _E total amount of -amylase produced (KNU) - substrate uptake (g substrate/(g cell massh)) - specific growth rate of cell mass (h^–1) - _d specific death rate of cells (h^–1) - _m maximum specific growth rate of cell mass (h^–1) This study was supported by Bioprocess Engineering Programme of the Nordic Industrial Foundation and the Center for Process Biotechnology, the Technical University of Denmark.     

On the appropriateness of use of a continuous formulation for the modelling of discrete multireactant systems following Michaëlis–Menten kinetics

The possibility of solving the mass balances to a multiplicity of substrates within a CSTR in the presence of a chemical reaction following Michaelis-Menten kinetics using the assumption that the discrete distribution of said substrates is well approximated by an equivalent continuous distribution on the molecular weight is explored. The applicability of such reasoning is tested with a convenient numerical example. In addition to providing the limiting behavior of the discrete formulation as the number of homologous substrates increases, the continuous formulation yields in general simpler functional forms for the final distribution of substrates than the discrete counterpart due to the recursive nature of the solution in the latter case.List of Symbols C{N. M} mol/m³ concentration of substrate containing N monomer residues each with molecular weight M - {N, M} normalized value of C{N. M} - C {M} mol/m³ da concentration of substrate of molecular weight M - _in normalized value of C {M} at the i-th iteration of a finite difference method - {M} normalized value of C {M} - C ₀{N.M} mol/m³ inlet concentration of substrate containing N monomer residues each with molecular weight M - {N ·M} normalized value of C₀{N. M} - _{0 i} normalized value of C ₀ {M} at the i-th iteration of a finite difference method - C ₀ {M} mol/m³ da initial concentration of substrate of molecular weight M - C _tot mol/m³ (constant) overall concentration of substrates (discrete model) - C _tot mol/m³ (constant) overall concentration of substrates (continuous model) - D deviation of the continuous approach relative to the discrete approach - i dummy integer variable - I arbitrary integration constant - j dummy integer variable - k dummy integer variable - K _m mol/m³ Michaëlis-Menten constant for the substrates - l dummy integer variable - M da molecular weight of substrate - M normalized value of M - M da maximum molecular weight of a reacting substrate - N number of monomer residues of a reacting substrate - N maximum number of monomer residues of a reacting substrate - N total number of increments for the finite difference method - Q m³/s volumetric flow rate of liquid through the reactor - S inert product molecule - S _i substrate containing i monomer residues - V m³ volume of the reactor - v _max mol/m³ s reaction rate under saturating conditions of the enzyme active site with substrate - v _max{N. M} mol/m³ s reaction rate under saturating conditions of the enzyme active site with substrate containing N monomer residues with molecular weight M - _max{N · M} dimensionless value of v_max{N. M} (discrete model) - _max{M} dimensionless value of v _max {M} (continuous model) - mol/m³ s molecular weight-averaged value of v_max (discrete model) - mol.da/m³s molecular weight-averaged value of v_max (continuous model) - v _max {M} mol.da/m³s reaction rate under saturating conditions of the enzyme active site with substrate with molecular weight M - _max {M} dimensionless value of v_max{M} - _{max, (i)} dimensionless value of v_max{M} at the i-th iteration of a finite difference method - v _max mol/m³ s reference constant value of v _max Greek Symbols dimensionless operating parameter (discrete distribution) - dimensionless operating parameter (continuous distribution) - M da (average) molecular weight of a monomeric subunit - M selected increment for the finite difference method - auxiliary corrective factor (discrete model)     

Evaluation of sensors for the control of a continuous ethanol fermentation

A method is presented for the evaluation of sensors used in the control of continuous fermentations. Simulations of open-loop response to input disturbance provided a starting point for the choice of sensor type. This was evaluated quantitatively through a sensitivity ratio. It was shown that in the case of ethanol fermentation, there existed three regions where different sensors could be used for the process control depending on the inlet sugar concentration. Sugar sensors were preferable above an inlet sugar concentration of 50 kg/m³, while ethanol sensors were preferable below 25 kg/m³. In the intermediate region, sugar and ethanol sensors demonstrated equally good performance. A controllability study of a continuous ethanol fermentation was also made. A single-stage continuous stirred-tank fermentor was simulated operating at a dilution rate of 0.1 1/h and inlet glucose concentration of 160 kg/m³. The outlet glucose concentration was controlled with a PI controller. Mean square error of the controller input signal during the first five hours after introducing input disturbance was taken as a measure of the controllability. This was studied in the relation to the two key sensor characteristics, sampling time and accuracy.List of Symbols c _p kg/m³ ethanol concentration - c _p kg/m³ fermentor ethanol concentration corresponding to c _si and D - c _s kg/m³ substrate (glucose) concentration - c _s kg/m³ fermentor glucose concentration corresponding to c _si and D - c _si kg/m³ inlet substrate (glucose) concentration - c _si kg/m³ inlet glucose concentration value used for sensitivity evaluation - c _sm kg/m³ glucose concentration — measured value - c _ss kg/m³ glucose concentration setpoint value - c _x kg/m³ biomass concentration - D 1/h dilution rate - D 1/h dilution rate value used for sensitivity evaluation - D _i 1/h dilution rate at ith sampling interval - D ₀ 1/h dilution rate at steady state - K _c m³/kgh controller gain - K _p kg/m³ product inhibition constant - K _s kg/m³ Monod constant - n ₁, n ₂ random numbers - r _p kg/m³ h ethanol production rate - r _s kg/m³ h substrate (glucose) consumption rate - r _x kg/m³ h biomass growth rate - vector of independent variables - y _i ith dependent variable - Y _ps ethanol yield - Y _xs biomass yield - parameter vector - _j jth parameter - _ij sensitivity of y_i with respect to _j - _p sensitivity of fermentor ethanol concentration - _s sensitivity of fermentor glucose concentration - sensitivity ratio - c _p kg/m³ ethanol concentration difference corresponding to a change of c _si by 5% - c _s kg/m³ glucose concentration difference corresponding to a change of c _si by 5% - c _si kg/m³ concentration difference added to c _si - _i kg/m³ error at ith sampling interval - 1/h specific growth rate - _m 1/h maximum specific growth rate - _s kg/m³ standard deviation of monitored glucose concentration - _I h min kg/m³ integral time - _s min sampling period The Swedish Ethanol Foundation and the National Board for Technical Development (NUTEK) are kindly acknowledged for the financial support of this project. The authors wish to thank Peter Warkentin for the linguistic advice.     

The effects of fermentation conditions on yeast cell debris particle size distribution during high pressure homogenisation

Experiments were performed to characterize the particle size distribution of bakers' yeast cells during high pressure homogenisation. Results were obtained for mechanically agitated batch and continuously grown cultures under a range of operating conditions. It was found that the dependency of cell debris size distribution on the number of passes through the homogeniser and the homogeniser pressure was independent of the cell properties and culture conditions, but for a fixed pressure and number of passes the extent of disruption was strongly affected by the operating conditions in the fermenter. The entire cell debris size distributions were successfully simulated using the mean and variance of the distributions and a previously published model equation which related these parameters to the operating pressure and number of passes through the homogeniser.List of Symbols k breakage coefficient in Eq. 1 - d cell diameter - d ₅₀ median diameter of homogenate size distribution - d ₅₀ dimensionless d ₅₀ defined as - D dilution rate - F(d _NP) cumulative undersize distribution (volume basis) - N number of passes - P total pressure - P _threshold threshold pressure - P (P-P _threshold) - w Boltzmann parameter, Eq. 4 - w dimensionless standard deviation defined as Greek Letters exponent in Eq. 1 - exponent in Eq. 1 UCL is the Biotechnology and Biological Sciences Research Council's Interdisciplinary Research Centre for Biochemical Engineering and the Council's support to the participating UCL departments is gratefully acknowledged. The provision of continuous fermentation material from Dr. M. Gregory, Process System Engineering IRC, is gratefully acknowledged.     

Observer design for differential-algebraic model of an aerobic culture of a recombinant yeast

The mathematical model of an aerobic culture of recombinant yeast presented in work by Zhang et al. (1997) is given by a differential-algebraic system. The classical nonlinear observer algorithms are generally based on ordinary differential equations. In this paper, first we extend the nonlinear observer synthesis to differential-algebraic dynamical systems. Next, we apply this observer theory to the mathematical model proposed in Zhang et al. (1997). More precisely, based on the total cell concentration and the recombinant protein concentration, the observer gives the online estimation of the glucose, the ethanol, the plasmid-bearing cell concentration and a parameter that represents the probability of plasmid loss of plasmid-bearing cells. Numerical simulations are given to show the good performances of the designed observer.Symbols C ₁ activity of pacing enzyme pool for glucose fermentation (dimensionless) - C ₂ activity of pacing enzyme pool for glucose oxidation (dimensionless) - C ₃ activity of pacing enzyme pool for ethanol oxidation (dimensionless) - E ethanol concentration (g/l) - G glucose concentration (g/l) - k _a regulation constant for (g glucose/g cell h^–1) - k _b regulation constant for (dimensionless) - k _c regulation constant for (g glucose/g cell h^–1) - k _d regulation constant for (dimensionless) - K _m1 saturation constant for glucose fermentation (g/l) - K _m2 saturation constant for glucose oxidation (g/l) - K _m3 saturation constant for ethanol oxidation (g/l) - L ( t) time lag function (dimensionless) - p probability of plasmid loss of plasmid-bearing cells (dimensionless) - P recombinant protein concentration (mg/g cell) - q _G total glucose flux culture time (g glucose/g cell h) - t culture time (h) - t _lag lag time (h) - X total cell concentration (g/l) - X ⁺ plasmid-bearing cell concentration (g/l) - Y ^F _{X / G} cell yield for glucose fermentation pathway (g cell/g glucose) - Y ^O _{X / G} cell yield for glucose oxidation pathway (g cell/g glucose) - Y _{X / E} cell yield for ethanol oxidation pathway (g cell/g ethanol) - Y _{E / X} ethanol yield for fermentation pathway based on cell mass (g ethanol·g cell) - ₂ glucoamylase yield for glucose oxidation (units/g cell) - ₃ glucoamylase yield for ethanol oxidation (units/g cell) - µ₁ specific growth rate for glucose fermentation (h^–1) - µ₂ specific growth rate for glucose oxidation (h^–1) - µ₃ specific growth rate for ethanol oxidation (h^–1) - µ_1max maximum specific growth rate for glucose fermentation (h^–1) - µ_2max maximum specific growth rate for glucose oxidation (h^–1) - µ_3max maximum specific growth rate for ethanol oxidation (h^–1)     

Optimizing control of a continuous stirred tank fermenter using a neural network

Feedforward neural networks are a general class of nonlinear models that can be used advantageously to model dynamic processes. In this investigation, a neural network was used to model the dynamic behaviour of a continuous stirred tank fermenter in view of using this model for predictive control. In this system, the control setpoint is not known explicitly but it is calculated in such a way to optimize an objective criterion. The results presented show that neural networks can model very accurately the dynamics of a continuous stirred tank fermenter and, the neural model, when used recursively, can predict the state variables over a long prediction horizon with sufficient accuracy. In addition, neural networks can adapt rapidly to changes in fermentation dynamics.List of Symbols F Dimensionless flow rate (F/ V₀) - F m³/h Flow rate - F ₀ m³/h Inlet flow rate - J Objective cost function - K _i Dimensionless constant in Eq. (3) (k _i /s₀) - k _i kg/m³ Substrate inhibition constant in Haldane model - k _m Dimensionless constant in Eq. (3) (k _s /s₀) - k _m kg/m³ Substrate inhibition constant in Haldane model - n prediction horizon - S Dimensionless substrate concentration (s/s₀) - s kg/m³ Substrate concentration - t h Time - v Dimensionless volume (V/V₀) - V m³ Liquid volume in fermenter - W _ij , W _jk Weight matrices in neural network - X Dimensionless biomass concentration - x kg/m³ Biomass concentration - Y Biomass/substrate yield coefficient - Weighting factor in Eq. (4) - Dimensionless specific growth rate (/ ) - 1/h Maximum specific growth rate - 1/h Specific growth rate - Dimensionless time ( t)     

The effect of carbon dioxide on the growth kinetics of fructose-limited chemostat cultures of Acetobacterium woodii DSM 1030

The growth of the anaerobic acetogenic bacterium Acetobacterium woodii DSM 1030 was investigated in fructose-limited chemostat cultures. A defined medium was developed which contained fructose, mineral salts, cysteine · HCl and Ca pantothenate (1 mg · 1^–1) supplied in a vitamin supplement. Growth at high dilution rates was dependent on the presence of CO₂ in the gas phase. The ^max was found to be 0.16 h^–1 and the fructose maintenance requirement was 0.1 to 0.13 mmol fructose · (g dry wt)^–1 · h^–1. A growth yield of 61 g dry wt · (mol fructose)^–1, corrected for the cell maintenance requirement and for incorporation of fructose carbon into cell biomass, was determined from the fructose consumption. A corresponding growth yield of 69 g dry wt · (mol fructose)^–1 was calculated from the acetate production assuming that fructose fermentation was homoacetogenic. A Y_ATP of 12.2 to 13.8 g dry wt · (mol ATP)^–1 was calculated from these growth yields using a value of 5 mol ATP · (mol fructose)^–1 as an estimate of the amount of ATP synthesised from fructose fermentation. The addition of yeast extract (0.5 g · 1^–1) to the medium did not influence the ^max or cell yield. After prolonged growth under fructose-limited conditions the requirement of the culture for CO₂ in the gas phase was reduced.Abbreviations YE yeast extract - IC inorganic carbon - D fermenter dilution rate : h^–1 - M_X maintenance requirement for X: mmol X · (g dry wt)^–1 · h^–1 - X may be fructose (Fruct), fructose consumed in energy metabolism (Fruct [E]), acetate (Ac) - ATP CO₂, NH _inf4 ^sup+ or Pi - qX specific rate of utilisation or consumption of X: mmol X · (g dry wt)^–1 · h^–1 - V fermenter volume: litre - rC · Cell, fermenter cell carbon production: mmol C · h^–1 - Y_X yield of cells on X: g dry wt · (mol X)^–1 - Y _infx ^supmax the yield corrected for cell maintenance: g dry wt · (mol X)^–1 - S_ATP stoichiometry of ATP synthesis from fructose: mol ATP · (mol frucose)^–1 - x cell concentration: g dry wt · 1^–1 - specific growth rate : h^–1 - ^max maximum specific growth rate: h^–1     

Continuous and biomass recycle fermentations of Clostridium acetobutylicum

Using experimental data from continuous cultures of Clostridium acetobutylicum with and without biomass recycle, relationships between product formation, growth and energetic parameters were explored, developed and tested. For glucose-limited cultures the maintenance models for, the Y _ATP and biomass yield on glucose, and were found valid, as well as the following relationships between the butanol (Y _B/G) or butyrate (Y _BE/G) yields and the ATP ratio (R _ATP, an energetic parameter), Y _B/G =0.82-1.35 R _ATP, Y _BE/G =0.54 + 1.90 R _ATP. For non-glucose-limited cultures the following correlations were developed, Y _B/G =0.57-1.07 , Y _B/G =0.82-1.35 R _ATPATP and similar equations for the ethanol yield. All these expressions are valid with and without biomass recycle, and independently of glucose feed or residual concentrations, biomass and product concentrations. The practical significance of these expressions is also discussed.List of Symbols D h^–1 dilution rate - m _e mol g^–1 h^–1 maintenance energy coefficient - m _G mol g^–1 h^–1 maintenance energy coefficient - R biomass recycle ratio, (dimensionless) - R _ATP ATP ratio (eqs.(5), (10) and (11)), (dimensionless) - X kg/m³ biomass concentration - Y _ATP g biomass per mol ATP biomass yield on ATP - Y _ATP ^max g biomass per mol ATP maximum Y _ATP - Y _A/G mol acetate produced per mol glucose consumed molar yield of acetate - y _an/g mol acetone produced per mol glucose consumed molar yield of acetone - Y _B/G mol butanol produced per mol glucose consumed molar yield of butanol - y _be/g mol butyrate produced per mol glucose consumed molar yield of butyrate - Y _E/G mol ethanol produced per mol glucose consumed molar yield of ethanol - Y _X/G g biomass per mol glucose consumed biomass yield on glucose - Y _ATP ^max g biomass per mol maximum Y _X/G glucose consumed - h^–1 specific growth rate     

Diagnosing lactic acid fermentation based on specific rates of growth,substrate consumption and product formation

The on-line calculated specific rates of growth, substrate consumption and product formation were used to diagnose microbial activities during a lactic acid fermentation. The specific rates were calculated from on-line measured cell mass, and substrate and product concentrations. The specific rates were more sensitive indicators of slight changes in fermentation conditions than such monitored data as cell mass or product concentrations.List of Symbols 1/h specific rate of cell growth - 1/h specific rate of substrate consumption - 1/h specific rate of product formation - ^* dimensionless specific rate of cell growth - ^* dimensionless specific rate of substrate consumption - ^* dimensionless specific rate of product formation - _max 1/h maximum specific rate of cell growth - _max 1/h maximum specific rate of substrate consumption - _max 1/h maximum specific rate of product formation - X g/l cell mass concentration - S g/l substrate concentration - S ^* dimensionless substrate concentration - S ₀ g/l initial substrate concentration - P g/l product concentration     

Enhancement of product selectivity via enzyme immobilization in sequential degradation reactions of polymeric substrates

The balance equations pertaining to the modelling of a slap-shaped bead containing immobilized enzyme uniformly distributed which catalyzes the sequential reactions of degradation of a polymeric substrate were written and analytically solved in dimensionless form. The effect of the Thiele modulus on the selectivity of consumption of each multimeric product was studied for a simple case. Whereas plain diffusional regime leads to lower selectivities than plain kinetic regime, improvements in selectivity of species A _i relative to species A_i+1 may be obtained at the expense of higher Thiele moduli within a limited range when the diffusivity of A _i is larger than that of A _i +1, or when the pseudo first order kinetic constant describing the rate of consumption of A _i is lower than that of A_i+1.List of Symbols A _i polymeric substrate containing i monomeric subunits - C _i mol·m^–3 normalized counterpart of C _i - C _i mol·m^–3 concentration of substrate A _i - C _i,0 mol·m^–3 initial concentration of substrate A _i - C _i,0 normalized counterpart of C _i,0 - D _ap,i m²·s^–1 apparent diffusivity of substrate A _i - k _i s^–1 pseudo-first order rate constant - K _m,i mol·m^–3 Michaelis-Menten constant associated with substrate A _i - L m half-thickness of the catalyst slab - N number of monomeric subunits of the largest substrate molecule - Th Thiele modulus - V _i mol·m^–3·s^–1 rate of rection of substrate A _i - V_max,i mol·m^–3·s^–1 maximum rate of reaction under saturating conditions of substrate A _i - x m longitudinal coordinate - S _i,i+1 selectivity of enzyme with respect to substrates with consecutive numbers of monomeric subunits Greek Symbols _i ratio of maximum rates of reaction - _i ratio of apparent diffusivities     

Product inhibition during the feeding phasein fed-batch ethanol fermentation of sugar-cane blackstrap molasses

Summary The following equations represent the influence of the ethanol concentration (E) on the specific growth rate of the yeast cells () and on the specific production rate of ethanol () during the reactor filling phase in fed-batch fermentation of sugar-cane blackstrap molasses: = ₀ - k · E and v = v ₀ · K/(K +E) Nomenclature E ethanol concentration in the aqueous phase of the fermenting medium (g.L^–1) - E_m value of E when = 0 or = 0 (g.L^–1) - F medium feeding rate (L.h^–1) - k empirical constant (L.g^–1.h^–1) - K empirical constant (g.L^–1) - M_as mass of TRS added to the, reactor (g) - M_cs mass of consumed TRS (g) - M_e mass of ethanol in the aqueous phase of the fermenting medium (g) - M_s mass of TRS in the aqueous phase of the fermenting medium (g) - M_x mass of yeast cells (dry matter) in the fermenting medium (g) - r correlation coefficient - S TRS concentration in the aqueous phase of the fermenting medium (g.L^–1) - S_m TRS concentration of the feeding medium (g.L^–1) - t time (h) - T temperature (° C) - TRS total reducing sugars calculated as glucose - V volume of the fermenting medium (L) - V₀ volume of the inoculum (L) - X yeast cells concentration (dry matter) in the fermenting medium (g.L^–1) - filling-up time (h) - specific growth rate of the yeast cells (h^–1) - ₀ value of when E=0 - specific production rate of ethanol (h^–1) - ₀ value of when E=0 - density of the yeast cells (g.L^–1) - dry matter content of the yeast cells     

Effect of dilution rate on the release of pertussis toxin and lipopolysaccharide ofBordetella pertussis

Summary The kinetics ofBordetella pertussis growth was studied in a glutamate-limited continuous culture. Growth kinetics corresponded to Monod's model. The saturation constant and maximum specific growth rate were estimated as well as the energetic parameters, theoretical yield of cells and maintenance coefficient. Release of pertussis toxin (PT) and lipopolysaccharide (LPS) were growth-associated. In addition, they showed a linear relationship between them. Growth rate affected neither outer membrane proteins nor the cell-bound LPS pattern.Nomenclature X cell concentration (g L^–1) - specific growth rate (h^–1) - _m maximum specific growth rate (h^–1) - D dilution rate (h^–1) - S concentration of growth rate-limiting nutrient (glutamate) (mmol L^–1 or g L^–1) - Ks substrate saturation constant (mol L^–1) - m_s maintenance coefficient (g g^–1 h^–1) - Y_x/s theoretical yield of cells from glutamate (g g^–1) - Y_x/s yield of cells from glutamate (g g^–1) - Y_PT/s yield of soluble PT from glutamate (mg g^–1) - Y_KDO/s yield of cell-free KDO from glutamate (g g^–1) - Y_PT/x specific yield of soluble PT (mg g^–1) - Y_KDO/x specific yield of cell-free KDO (g g^–1) - q_PT specific soluble PT production rate (mg g^–1 h^–1) - q_KDO specific cell-free KDO production rate (g g^–1 h^–1)     

Influence of exponentially decreasing feeding rates on fed-batch ethanol fermentation of sugar cane blackstrap molasses

Summary The ethanol yield was not affected and the ethanol productivity was increased when exponentially decreasing feeding rates were used instead of constant feeding rates in fed batch ethanol fermentations. The influences of the initial sugar feeding rate on the ethanol productivity, on the constant ethanol production rate during the feeding phase and on the initial ethanol production specific rate are represented by Monod-like equations.Nomenclature F reactor feeding rate (L.h^–1) - F_o initial reactor feeding rate (L.h^–1) - K time constant; see equation (l) (h^–1) - M_E mass of ethanol in the fermentor (g) - M_s mass of TRS in the fermentor (g) - M_x mass of yeast cells (dry matter) in the fermentor (g) - P ethanol productivity (g.L^–1.h^–1) - R ethanol constant production rate during the feeding phase (g.h^–1) - s standard deviation - S_o TRS concentration in the feeding mash (g.L^–1) - t time (h) - T fermentor filling-up-time (h) - T time necessary to complete the fermentation (h) - TRS total reducing sugars calculated as glucose (g.L^–1) - V_o volume of the inoculum (L) - V_f final volume of medium in the fermentor (L) - X_o yeast concentration of the inoculum (dry matter) (g.L^–1) - ethanol yield (% of the theoretical value) - initial specific rate of ethanol production (h^–1)     

Biodegradation of naphthalenesulphonic acid-containing sewages in a two-stage treatment plant

The production of naphthol the coupling compound in the syntheses of azo-dyes occurs a naphthalenesulphonic acid-containing wastewater. The aerobic biodegradation of a complex mixture of naphthalenemono- and -disulphonic acids with high amounts of inorganic salts was examined in a two-stage plant with specially adapted and immobilized microorganisms fixed on broken sand particles. The plant consists of two airlift-loop reactors. An interposed settling tank separates the two different bacterial communities in the stages. In the first stage the sequential metabolization of naphthalene-2- and-1-sulphonic acid was achieved by strain Pseudomonas testosteroni A3 at residence times down to 1.5 h. The total degradation of remaining naphthalene-1-sulphonic acid and the degradation of recalcitrant naphthalenedisulphonic acids was obtained by a defined mixed culture in the second unit. Because of the more recalcitrant character of the remaining components in the second stage examinations with Na₂SO₄-loaded and salt-free wastewater were carried out at mean residence times between 50 and 6.3 h. With salt-loaded sewage an overall degradation of approximately 71% was achieved. The main component in the effluent was non-biodegradable naphthalene-1.5-disulphonic acid. Investigations with salt-free wastewater have shown an increasing overall degradation up to 84%. Thus, in the presence of inorganic salts a considerable inhibition of the biological degradation of the recalcitrant substances in the second unit was found.List of Symbols 1NS naphthalene-1-sulphonic acid - 2NS naphthalene-2-sulphonic acid - 1.5NDS naphthalene-1.5-disulphonic acid - 1.6NDS naphthalene-1.6-disulphonic acid - 2.6NDS naphthalene-2.6-disulphonic acid - 2.7NDS naphthalene-2.7-disulphonic acid - 6A2NS 6-amino-naphthalene-2-sulphonic acid - D 1/h dilution rate - K _s mg/l Monod coefficient - m _s mg_s/(h g_BM) maintenance coefficient - NDS naphthalenedisulphonic acids - NS naphthalenemonosulphonic acids - NSS total naphthalenesulphonic acids - Pr mg/(h l) substrate degradation rate - Pr substrate degradation rate in dimensionless form - S mg/l substrate concentration - S _E mg/l substrate input concentration - u _g cm/s superviciai gas velocity - X _f g/l free biomass concentration - X _i g/l immobilized biomass concentration - Y _X/s g_BM/g_s] substrate yield coefficient - X_i/ (K_s Y_X/S) immobilized biomass concentration in dimensionless form - 1/h specific growth rate - _max 1/h maximum specific growth rate     

Respiratory activity and growth kinetics of Candida yeasts related to carbon sources and available energy

Summary Three yeasts of the genus Candida (Candida intermedia, candida lipolytica and Candida tropicalis) were cultivated batchwise on three different carbon sources: glucose, acetate, and hexadecane. Growth curves, oxygen uptake rates, CO₂ evolution rates and the amount of oxygen required for biomass production were determined. The data were compared and discussed from the point of maximum specific growth rate, maximum oxygen uptake rate, carbon conversion into CO₂ and biomass, consumption of oxygen and available energy for cell synthesis. The results indicated a relationship between _m m, Y_s, Y_O, and for different carbon sources. Y_O and were in the same order of magnitude for acetate (0.58 and 0.38 respectively) and hexadecane (0.45 and 0.40 respectively). These values were remarkably lower than those for glucose (1.26 and 0.54 respectively).Symbols av e^– Available electrons per mol of substrate (dimensionless) - E_av Energy available per mol of substrate (dimensionless) - C_d Dissimilated carbon (%) - m Maximum specific rate of oxygen uptake (mMO₂ h^–1 g^–1) - RQ CO₂ evolved per O₂ consumed - mol. wt. Molecular weight - Y_ATP Biomass mass yield based on mol of ATP generated (g) - Biomass mass yield based on available energy (g) - Y_M Biomass mass yield based on mol of organic substrate (g) - Y_O Biomass mass yield based on oxygen consumed (gg^–1) - 1/Y_O Oxygen consumed for one gram of biomass produced (gg^–1) - Y_s Biomass mass yield based on organic substrate (dimensionless) - b Reductance degree of biomass (equiv. available electrons/g atom carbon) - s Reductance degree of organic substrate (equiv. available electrons/g atom carbon) - Fraction of energy in organic substrate which is converted to biomass - b Weight fraction carbon in biomass (dimensionless) - s Weight fraction carbon in organic substrate (dimensionless) - _m Maximum specific growth rate (h^–1)     

A fedbatch strategy for optimal red pigment production by monascus ruber

According to the measurement of the pigment production and some material balance treatments, the monosodium glutamate (MSG), which represents a main substrate involved in the production of red pigment by Monascus ruber, is recovered on-line. Fedbatch operation then represents an alternative for increasing the production of pigment. A nonlinear quotient control scheme is expressed to regulate the monosodium glutamate substrate at an optimal value determined from batch studies.List of Symbols A absorbancy units (AU) - L lightness parameter - Pig red pigment quantity (Gmol) - vol fermentor active volume (1) - empirical coefficient - MW _pig red pigment molecular weight (g) - E elementary matrix - E ^# pseudo-inverse elementary matrix - r conversion rates vector (g· l^–1·h^–1) - E _m measured part of the elementary matrix - r _m measured conversion rates vector - E _c non-measured part of the elementary matrix - r _c non-measured conversion rates vector - v fictitious controller input - h fictitious controller output - u controller input - y controller output - y controller setpoint - k ₁ controller parameter - k ₂ controller parameter - k time iteration - MSG monosodium glutamate concentration (g·l^–1) - MSG _init monosodium glutamate initial quantity (g) - MSG _added total quantity of monosodium glutamate added (g) - MSG _cons total quantity of monosodium glutamate consumed (g) - MW _msg monosodium glutamate molecular weight (g)     

Application of material and energy balances in the interpretation of intermediate product build-up in batch growth of Pseudomonas aeruginosa on n-hexadecane

Summary This work is concerned with the application of material and energy balances in an attempt to understand the phenomenon of product build-up when Pseudomonas aeruginosa is grown on n-hexadecane in a batch fermentor. It is shown that the organism accumulates a polyactide, called poly-B-hydroxybutyrate (PHB) during early stages of growth and metabolizes it at later stages of growth. This explains the low carbon and available electron balances which have been observed.Nomenclature d Moles of carbon dioxide per quantity of organic substrate containing one g atom carbon, g mole/g atom carbon - m _e Rate of organic substrate consumption for maintenance, g equiv. of available electrons/g equiv. of available electrons in biomass (h) - Specific rate of evolution of carbon dioxide, g moles/g dry wt (h) - Specific rate of oxygen consumption, g mole/g dry wt (h) - s Organic substrate concentration, g/liter - t Time (h) - x Biomass concentration, g/liter - y _c Biomass carbon yield (fraction of organic substrate carbon in biomass), dimensionless - _b Reductance degree of biomass, equivalents of available electrons per g atom carbon - _s Reductance degree of substrate, equivalents of available electrons per g atom carbon - Fraction of energy in organic substrate which is evolved as heat, dimensionless - Fraction of energy in organic substrate which is coverted to biomass or biomass energetic yield, dimensionless - Specific growth rate, h^-1 - _b Weight fraction carbon in biomass, dimensionless - _s Weight fraction carbon in substrate, dimensionless     

Comparison of models for subtractive and shunting lateral-inhibition in receptor-neuron fields

Summary Two types of neuronal lateral inhibition in one-dimensional fields of receptors and neurons are considered. The first type, which has been demonstrated in the eye of Limulus, is called subtractive inhibition (SI): it assumes that neuronal activity depends on the difference between the total excitation and inhibition. The second type is called shunting inhibition (SHI): it assumes that inhibitory influences cause a shunting of a portion of the excitation-produced depolarizing current. Consideration of the shunting model is dictated by its considerable physiological plausibility. The actions of SI and SHI, examined for a variety of coupling conditions and time-stationary positive inputs, are shown to be markedly different. The results indicate that SI is most suited for obtaining (1) a linearity between input and output, (2) a contrasting effect that does not depend on the presence of input discontinuities, and (3) contrasting whose degree is independent of input amplitude. SI is especially useful if coupling coefficients can be varied to accommodate the various input form functions or if, for fixed coupling coefficients, the class of input form functions is limited. On the other hand SHI appears most suited for obtaining (1) a nonlinear input-output relation, (2) a relative contrasting only of discontinuities, and (3) a dependence of the contrasting upon input amplitude.List of Main Symbols a coupling coefficient for neighboring units, also called coupling amplitude - V _j output of receptor number j - i _j generator current of neuron number j - g inhibitory function for subtractive inhibition - h inhibitory function for shunting inhibition - v ₂/v ₁ [applies to two-unit case] - N _k neuron number k - I _k total source current produced by excitatory influences on N _k - G _k conductance for source current not shunted (with shunting inhibition) - i portion of source current shunted as a result of inhibition - m number of inhibitory influences [in Eq. (1)] - G _kj conductance of inhibitory shunt path j for neuron N _k - q number of receptors - n number of neurons - R _j receptor number j - x distance - y(x) input stimulus to receptors - y _j =y(x _j ) input stimulus to receptor R _j - v _j v_j for v _j 0, zero otherwise - a _kj G _kj /v _j , inhibitory coupling coefficient for forward shunting inhibition [refer to Eq. (2)] - b _kj excitatory coupling coefficient for contribution to source current of neuron N _k by receptor R _j [refer to Eq. (3)] - i _j i _j for i _j 0, zero otherwise - c _kj G _kj /i _j , inhibitory coupling coefficient for backward shunting inhibition [refer to Eq. (4)] - â _kj inhibitory coupling coefficient for forward subtractive inhibition [refer to Eq. (5)] - _kj inhibitory coupling coefficient for backward subtractive inhibition [refer to Eq. (6)] - y(x _j )=Af(x _j ) sensory input function - A input amplitude - f(x _j ) sensory input form function, also called a sensory image - i(x _j ) generator current output of neuron Nj which is located at x=x _j - y (y ₁, y ₂, ..., y _n), a column vector - i (i ₁, i ₂, ..., i _n), a column vector, also called generator current configuration - a an n by n matrix having a _kj as the term in the k-th row, j-th column - U the unit matrix - d ¦k-j¦, separation between neurons N _k and N _j - a a _kj for d=1, called coupling amplitude - SI subtractive inhibition - SHI shunting inhibition - FSI forward subtractive inhibition - BSI backward subtractive inhibition - FSHI forward shunting inhibition - BSHI backward shunting inhibition - s i/i ₅₁ = (s ₁, s ₂, ..., s _n), normalized generator current vector, also called normalized generator current configuration - s _j i _j/i ₅₁, normalized generator current of neuron N _j - f(x) continuous input form function of which f(x _j ) is a sampled version - ^p f(x)/x ^p p-th order derivative of f(x)     

Biotransformation of cephalosporin C to 7-aminocephalosporanic acid with coimmobilized biocatalyst in a batch bioreactor

Biotransformation of cephalosporin C (CPS-C) to 7-aminocephalosporanic acid (7-ACA) was carried out with coimmobilized permeabilized cells of Trigonopsis variabilis and Pseudomonas species entrapped in Ca-pectate gel beads. Good aeration and stirring during the process was assured. The analysis of this complicated biochemical process in a heterogeneous system was based on the identification of individual effects (internal diffusion, reaction) running simultaneously. A spectrophotometric method was proposed for the determination of 7-(-ketoadipyl amido) cephalosporanic acid (CO-GL-7-ACA) and 7-ACA. The reaction-diffusion model containing dimensionless partial differential equations was solved by using the orthogonal collocation method. A good agreement between experimental values and values predicted by the mathematical model was obtained. Numerical simulations were performed on the basis of following the two assumptions:- several times higher activity of both cells,- hydrogen peroxide was continuously supplied in the bioreactor.List of Symbols A m² surface of the bead - c _i mol/dm³ concentration of component in the bead and/or in the solution - c _i0 mol/dm³ initial concentration of component in the solution - c _l0 mol/dm³ initial concentration of CPS-C in the solution - C _jl orthogonal collocation weights of the first derivation - D _ei m²/s effective diffusion coefficient of the components - D _jl orthogonal collocation weights of the second derivation - k ₅ dm³/(mol · s) kinetic parameter of non-enzyme reaction - K _inh mol/dm³ inhibition parameter for the first enzyme reaction - K _i dimensionless Michaelis constant for the first and second enzyme reaction, defined in Eq. (7) - K _l dimensionless inhibition parameter for the first enzyme reaction, defined in Eq. (7) - K _mi mol/dm³ Michaelis constant for the first and second enzyme reaction - n number of beads - P( _i ) symbol of dimensionless reaction rate, defined in Eq. (13) - r m radial coordinate inside the bead - R m radius of the bead - R(c _i ) mol/(dm³ · s) symbol for reaction rate, defined in Eq. (6) - t s time - V _max mol/(dm³ · s) max. reaction rate for the first and second enzyme reaction - V _L dm³ volume of solution excluding the space occupied by beads - voidage in batch bioreactor - _P porosity of the bead - i dimensionless effective diffusion coefficient of the components, defined in Eq. (7) - dimensionless time, defined in Eq. (7) - _mi Thiele modulus, defined in Eq. (7) - _i dimensionless concentration, defined in Eq. (7) - dimensionless radial position inside the bead, defined in Eq. (7) - _l0 initial dimension concentration of CPS-C, defined in Eq. (9), (10) - _i0 initial dimension concentration of component, defined in Eq. (9), (10) The authors wish to thank Dr. P. Gemeiner of Slovak Academy of Sciences for rendering of pectate gel. This work is supported by Ministry of Education (Grant No. 1/990 935/93).